2.1345   ODE No. 1345

\[ y''(x)=\frac {2 y(x)}{x^4}-\frac {y'(x)}{x^3} \]

✓ Mathematica : cpu = 0.0409621 (sec), leaf count = 52

DSolve[Derivative[2][y][x] == (2*y[x])/x^4 - Derivative[1][y][x]/x^3,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{2 x^2}} x-\sqrt {\frac {\pi }{2}} c_2 e^{\frac {1}{2 x^2}} x \text {erf}\left (\frac {1}{\sqrt {2} x}\right )\right \}\right \}\]

✓ Maple : cpu = 0.064 (sec), leaf count = 25

dsolve(diff(diff(y(x),x),x) = -1/x^3*diff(y(x),x)+2/x^4*y(x),y(x))
 

\[y \left (x \right ) = x \,{\mathrm e}^{\frac {1}{2 x^{2}}} \left (\operatorname {erf}\left (\frac {\sqrt {2}}{2 x}\right ) c_{2} +c_{1} \right )\]